An Accurate Finite-Difference Method for Higher Order Waveguide Modes

The study of new waveguide shapes requires an accurate knowledge of their higher order modes for bandwidth consideration, waveguide discontinuity analysis, and multimode launching and propagation studies. The finite-difference method solved by successive overrelaxation is a very accurate and general technique for dominant mode solution. The method makes minimum demand on computer store, the number of storage locations required being equal to the order of the matrix defining the system of linear equations used. Convergence criteria require that this matrix be positive semidefinite. For modes higher than the dominant, the method fails to converge as this condition is violated. Solution is obtained by redefining the problem such that the matrix is positive semidefinite for all modes. An algorithm is described which produces one row at a time of the new matrix, as required for successive overrelaxation, and thus reserves almost all computer store for the eigenvector. The eigenvector elements give field potentials at discrete points in the guide cross section. Iteration for higher order modes is successfully applied with all the computational benefits realized by previous finite-difference schemes for the dominant mode. Examples studied are the rectangular, circular, asymmetric ridge, and lunar guides. Results for higher order cutoff wave numbers are usually accurate to within 0.1 percent.     

Attenuation Constant of Lunar Line and T-Septate Lunar Line

The attenuation constant /spl alpha/ of the lunar line and that of the T-septate lunar line were derived from the average power loss W/sub L/ and the average power transfer W/sub T/ in each line, that is the ratio, W/sub L//2W/sub T/. The average power loss and the average power transfer for the lunar line and for the T-septate lunar line were derived from their respective field functions. The theoretical attenuation constant of a typical lunar line is less than 0.7 db/ 100 ft for frequencies greater than 2000 Mc. The theoretical attenuation constant of a typical T-septate line is less than 0.9 db/ 100 f t for frequencies greater than 1000 Mc. Experimental measurements of the attenuation constant of a T-septate lunar line agree with the theoretical value. In the 200 to 2000 Mc frequency band, the lunar line and the T-septate lunar line offer a compact and light package without an appreciable sacrifice in peak power handling capacity or attenuation.     

Finite Element Analysis Waveguides of Optical

A finite element program for the analysis of anisotropic optical waveguides is described. The appearance of spurious numerical modes, due to the fact that the functional is nonpositive definite is discussed and a possible solution to the problem is presented. For isotropic waveguides it is shown that both EH- and HE-type modes can be very accurately approximated by two different scalar finite element programs. Finally, a method for calculating the attenuation of leaky modes in a single material integrated optic waveguide using this scalar finite element method is proposed.     

Performance of an array of circular waveguides with strip-loadeddielectric hard walls

An infinite planar periodic antenna array of radiating open-ended circular waveguides is considered. The conducting waveguide walls are covered with dielectric layers loaded with longitudinal conducting strips for providing the hard wall boundary condition. Analysis of the array is carried out by the mode-matching method. The waveguide modes involved in the method are calculated by using the asymptotic strip boundary condition. It is shown that they are split into an independent subsystem of TE modes for the whole cross section and two independent subsystems of TM modes: one is for the central region and another is for the layer region. The calculations show that the operation of the hard waveguides in an array with small element spacing is similar to that of the multimode smooth wall waveguides completely filled with dielectric. For large diameters and element spacing, the hard waveguides have significant advantages over the smooth ones. It is shown that unlike an individual hard waveguide, the aperture efficiency of such a waveguide in the array has a nonmonotonic dependence on the waveguide radius. The results characterizing the behavior of the aperture efficiency and cross-polarization level in a frequency band as well as the contribution of certain waveguide modes in the reflected power are presented and discussed. The examples of the element patterns corresponding to minimal cross polarization are also given     

Propagation in statistically irregular waveguides--Part I: Average field

The Green's function technique is employed to investigate the influence of the boundary condition perturbations in a number of wave propagation problems. The method permits treatment of multiple scattering on random irregularities of a boundary surface which is of particular importance for waveguide applications. For an average Green's function the Dyson type equation has been obtained whose solution represents the coherent part of a point source field in a rough waveguide. The eigenfunction spectrum has also been calculated for such waveguides. By means of mutual wave transformation due to the scattering, the waveguide modes acquire additional (lossless) damping and altered phase velocities. Detailed calculations have been carried through for plane acoustical waveguides with statistically rough walls under the Dirichlet and Neumann conditions. The average field's damping has also been considered for some cases of more complex geometry. In the electromagnetic case the electrical and magnetic solutions are similarly influenced by the wall roughness. Owing to the scattering they acquire longitudinal components ofEorHthus becoming guasi-electrical or quasi-magnetic. For these normal waves the damping coefficients (attenuation rates) have been derived. A particular attention is paid to cutoff frequencies in the presence of effective wave conversion to the resonant mode.     

AlGaAs-based two-dimensional photonic crystal slab with defectwaveguides for planar lightwave circuit applications

An AlGaAs-based near-infrared 2-D photonic crystal (PC) with an air-bridge structure featuring defect waveguides has been developed. For the sample without defect waveguides, measurements of the optical transmission characteristics in the wavelength range from 850 nm to 1100 nm showed a deep attenuation due to a bandgap with 30-35 dB attenuation and transmittance of nearly 100% for the guided modes. Optical propagation properties of defect waveguides were obtained by two methods: measurements of transmission spectra and plan-view observations of the optical beam trace along the waveguide with an infrared-vidicon camera. 3-D finite-difference time-domain simulations for the band structure and transmission spectra in the air-bridge slab with and without defect waveguides have revealed the appearance of four defect propagation modes specific to the defect waveguide, between two slab modes for the defect-free photonic crystal slab. These defect modes were experimentally identified in the measured transmission spectra     

Investigation of mode coupling due to ohmic wall losses inovermoded uniform and varying-radius circular waveguides by the methodof cross sections

The effect of ohmic wall losses on mode coupling in overmoded varying-radius circular waveguides is investigated. Mode coupling and multimode propagation in uniform lossy-wall circular waveguides is also discussed. The expressions for the coupling coefficients are given by line integrals of the power-normalized fields of the normal modes along the boundary of the waveguide cross section. Numerical results are presented for the case of propagation of an HE₁₁-like mode excitation in a uniform smooth lossy-wall circular waveguide     

Application of a Variation-Iteration Method to Waveguides with Inhomogeneous Lossy Loads

An approximate technique for solving eigenvalue equations, the variation-iteration method,is commonly used in theoretics physics. A previous paper presented the application of this method to the scalar case of a dielectric slab loaded rectangular waveguide. This paper presents its extension to the complex vector case of a lossy dielectric insert loaded waveguide. Starting from an initial trial function, iterates are calculated in which the components relative to the unwanted eigenfunctions are eliminated. Both an upper and a lower bound for the unknown eigenvalues are available. Each iterate is the solution of a system of algebraic simultaneous equations. This system is solved by the successive overrelaxation method using an automatically computed optimal accelerating factor. An extrapolation technique further accelerates the convergence. This yields the attenuation and propagation coefficients for the dominant as well as several other modes, together with the electric and magnetic field configurations.     

A linear-operator formalism for bianisotropic waveguides

A bianisotropic waveguide can be defined as a cylindrical waveguide filled with bianisotropic materials, and all the conventional waveguides are special cases of the bianisotropic waveguide. In this paper, guided wave propagation in bianisotropic waveguide is analyzed by the theory of linear operators, and two types of adjoint waveguides and inner products are introduced respectively. Based on the concept of adjoint waveguides, the functional expressions of the field equations can be obtained, and from which the eigenvalue problem of the bianisotropic waveguide can be solved. Also, bi-orthogonality relations of guided modes are derived. These biorthogonality relations reported here can be used to expand electromagnetic fields in terms of a complete set of modes in straight bianisotropic waveguide. As an example of application, mode matching formulae for a discontinuity problem are given.     

Modes and attenuation constants in circular hollow waveguides withsmall core diameters for the infrared

The mode structures and attenuation constants in circular hollow waveguides are evaluated numerically based on the exact characteristic equations. Mode properties, which are strongly dependent on waveguide materials, and attenuation constants are discussed when the core diameter becomes small. Special modes are also analyzed in oversized metallic waveguides which approach very familiar modes in perfectly conducting cylindrical waveguides when the core diameter becomes small     

High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners

For part I see ibid., p. 1210, 2002. We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a dielectric corner. Although certain components of the electric field have long been known to be infinite at the corner, it is shown that all components of the magnetic field are finite, and that finite-difference equations may be derived for these fields that satisfy correct boundary conditions at the corner. These finite-difference equations have been combined with those derived in the previous paper to form a full-vector waveguide solution algorithm of unprecedented accuracy. This algorithm is employed to provide highly accurate solutions for the fundamental modes of a previously studied standard rib waveguide structure.     

Low-Loss Two-Dimensional GaAs Epitaxial Waveguides at 10.6-/spl mu/m Wavelength

The successful fabrication of low-loss two-dimensional GaAs epitaxial waveguides by chemical etching for use in integrated optics at 10.6 /spl mu/m is reported. Selective excitation of specific E/sub pq//sup y/ modes was observed by placing the prism at specific angles in the horizontal plane. Loss measurements showed no increase in attenuationfor lower order E/sub pq//sup y/ modes (as compared to corresponding one-dimensional waveguide modes) when the guide width is 50 /spl mu/m. As the guide width is reduced, there is a significant increase in attenuation as p increases.     

Biharmonic Operators for the Waveguide Problem (Correspondence)

The inverse iteration method of analyzing an isotropic waveguide is reexamined with a view to finding the higher order modes. It is shown that the problem may be formulated in terms of a generalized biharmonic operator, which is always at least semidefinite. Several finite-difference representations are given for this operator. Of these, two possess property A, a point of fundamental importance for iterative solution by successive overrelaxation.     

手征等离子体填充圆波导的传播特性

本文在柱坐标系中导出了手征等离子体波导内横向场量与纵向场量之间的关系,给出求解纵向场量的波动方程.利用波导壁上的电场边界条件,建立了手征等离子体介质填充的圆波导传播常数的特征方程,计算得到了几种低次模式的传播常数随归一化波导半径及材料参数的一系列变化曲线,分析得出了若干有意义的结论.     

基于矢量有限元的任意介质加载波导通用软件设计

本文旨在实现波导问题的通用软件设计,文章完善了各向异性介质填充波导问题的矢量有限元理论,并计算了有耗、各向异性介质加载的任意结构波导模式传输系数、色散曲线和模式电场分布。在计算色散曲线时,本文结合了模式场图以消除HFSS在色散计算过程中对传输模式的误判。对于开放结构波导,采用各项异性介质的完全匹配层（PML）理论实现无限的问题截断。通过与商业电磁仿真软件的计算结果作比较,验证了算法的精确性。     

Poling-induced waveguide polarizers in electrooptic polymers

In order to demonstrate polymeric waveguide polarizers, photobleached polymer waveguides supporting both TE and TM modes are integrated with poling induced polymer waveguides that support either TE or TM modes. Fabrication parameters like UV exposures and poling voltages are controlled to reduce excess losses due to the mode profile mismatch between the connected waveguides. A TM-pass polarizer is realized by poling the polymer in the vertical direction. For TE-pass polarizer the polymer is poled horizontally by using four poling electrodes which enhance the uniformity of the poling field direction. The measured excess loss is less than 0.5 dB, and polarization extinction ratios for TM-pass and TE-pass polarizers are 20.7 dB and 17.1 dB, respectively.     

Transmission Characteristics of Hybrid Modes in Corrugated Waveguides Above the Bragg Frequency

We studied the transmission characteristics of hybrid modes in a corrugated circular waveguide above the Bragg frequency to develop a broad-band transmission line for millimeter waves. Millimeter waves at 294 GHz were transmitted into a straight waveguide. From observed power profiles in waveguide cross-sections, a high attenuation rate of 0.13 dB/m was obtained. To match a theoretical attenuation constant with the experimental one, we introduced an ad hoc coefficient of conventional surface reactance in the waveguide wall. This was necessary because the wall began to look like the surface with a decreasing anisotropic reactance owing to the frequency above the Bragg frequency. Using nonlinear optimization for mode content analysis, the observed power profiles in the waveguide cross-section were matched with theoretical profiles. There was good agreement between the calculated and observed centers of power profiles and attenuation rate along the waveguide. The theoretical analysis showed that the magnetic field at the waveguide wall increases and the substantial attenuation takes place. Above the Bragg frequency coupling to backwards propagating modes is a point of consideration. A combination of the backwards propagating EH_1,26 and the forward propagating HE₁₁ modes satisfied the Bragg condition at 294.7 GHz which was the nearest frequency of operating frequency. A strong attenuation of the incoming HE₁₁ mode by Bragg resonance was not expected due to large difference of 0.7 GHz. It becomes clear that the observed high transmission loss outside of the Bragg resonance can be explained by a decrease in anisotropic surface reactance at the wall.     

Application of SSOR Preconditioning Technique to Method of Lines for Millimeter Wave Scattering

In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps.     

任意截面波导特性的非正交频域有限差分研究

本文提出了一种求解波导本征问题的非正交频域有限差分(FD-FD)算法。该算法中的数值离散网格可与任意复杂边界形状吻合一致。文中通过所建立的本征方程对波导中各模式的截止频率进行了求解,数值结果与已有结果符合良好。     

Analysis of Lossy Inhomogeneous Waveguides Using Shooting Methods (Short Papers)

Shooting methods are used to analyze rectangular waveguides containing inhomogeneous lossy dielectrics. The technique obtains the electromagnetic fields inside the waveguide by solving Maxwell's equations using trial and error procedures to match the boundary conditions at the conducting waveguide surface. Dispersion and attenuation curves are obtained which show how continuous dielectric inhomogeneities and losses affect the transmission characteristics of these waveguides.